Effects of reinforcer rate and reinforcer quality on time allocation: Extensions of matching theory to educational settings

We examined how 3 special education students allocated their responding across two concurrently available tasks associated with unequal rates and equal versus unequal qualities of reinforcement. The students completed math problems from two alternative sets on concurrent variable-interval (VI) 30-s VI 120-s schedules of reinforcement. During the equal-quality reinforcer condition, high-quality (nickels) and low-quality items ("program money" in the school's token economy) were alternated across sessions as the reinforcer for both sets of problems. During the unequal-quality reinforcer condition, the low-quality reinforcer was used for the set of problems on the VI 30-s schedule, and the high-quality reinforcer was used for the set of problems on the VI 120-s schedule. Equal- and unequal-quality reinforcer conditions were alternated using a reversal design. Results showed that sensitivity to the features of the VI reinforcement schedules developed only after the reinforcement intervals were signaled through countdown timers. Thereafter, when reinforcer quality was equal, the time allocated to concurrent response alternatives was approximately proportional to obtained reinforcement, as predicted by the matching law. However the matching relation was disrupted when, as occurs in most natural choice situations, the quality of the reinforcers differed across the response options.     

Tests of behavior momentum in simple and multiple schedules with rats and pigeons.

Four experiments examined the relationship between rate of reinforcement and resistance to change in rats' and pigeons' responses under simple and multiple schedules of reinforcement. In Experiment 1, 28 rats responded under either simple fixed-ratio, variable-ratio, fixed-interval, or variable-interval schedules; in Experiment 2, 3 pigeons responded under simple fixed-ratio schedules. Under each schedule, rate of reinforcement varied across four successive conditions. In Experiment 3, 14 rats responded under either a multiple fixed-ratio schedule or a multiple fixed-interval schedule, each with two components that differed in rate of reinforcement. In Experiment 4, 7 pigeons responded under either a multiple fixed-ratio or a multiple fixed-interval schedule, each with three components that also differed in rate of reinforcement. Under each condition of each experiment, resistance to change was studied by measuring schedule-controlled performance under conditions with prefeeding, response-independent food during the schedule or during timeouts that separated components of the multiple schedules, and by measuring behavior under extinction. There were no consistent differences between rats and pigeons. There was no direct relationship between rates of reinforcement and resistance to change when rates of reinforcement varied across successive conditions in the simple schedules. By comparison, in the multiple schedules there was a direct relationship between rates of reinforcement and resistance to change during most tests of resistance to change. The major exception was delivering response-independent food during the schedule; this disrupted responding, but there was no direct relationship between rates of reinforcement and resistance to change in simple- or multiple-schedule contexts. The data suggest that rate of reinforcement determines resistance to change in multiple schedules, but that this relationship does not hold under simple schedules.     

Multiple determinants of the effects of reinforcement magnitude on free-operant response rates

Four experiments examined the effects of increasing the number of food pellets given to hungry rats for a lever-press response. On a simple variable-interval 60-s schedule, increased number of pellets depressed response rates (Experiment 1). In Experiment 2, the decrease in response rate as a function of increased reinforcement magnitude was demonstrated on a variable-interval 30-s schedule, but enhanced rates of response were obtained with the same increase in reinforcement magnitude on a variable-ratio 30 schedule. In Experiment 3, higher rates of responding were maintained by the component of a concurrent variable-interval 60-s variable-interval 60-s schedule associated with a higher reinforcement magnitude. In Experiment 4, higher rates of response were produced in the component of a multiple variable-interval 60-s variable-interval 60-s schedule associated with the higher reinforcement magnitude. It is suggested that on simple schedules greater reinforcer magnitudes shape the reinforced pattern of responding more effectively than do smaller reinforcement magnitudes. This effect is, however, overridden by another process, such a contrast, when two magnitudes are presented within a single session on two-component schedules.     

Sensitivity to relative reinforcer rate in concurrent schedules: independence from relative and absolute reinforcer duration

Twelve pigeons responded on two keys under concurrent variable-interval (VI) schedules. Over several series of conditions, relative and absolute magnitudes of reinforcement were varied. Within each series, relative rate of reinforcement was varied and sensitivity of behavior ratios to reinforcer-rate ratios was assessed. When responding at both alternatives was maintained by equal-sized small reinforcers, sensitivity to variation in reinforcer-rate ratios was the same as when large reinforcers were used. This result was observed when the overall rate of reinforcement was constant over conditions, and also in another series of concurrent schedules in which one schedule was kept constant at VI ached 120 s. Similarly, reinforcer magnitude did not affect the rate at which response allocation approached asymptote within a condition. When reinforcer magnitudes differred between the two responses and reinforcer-rate ratios were varied, sensitivity of behavior allocation was unaffected although response bias favored the schedule that arranged the larger reinforcers. Analysis of absolute response rates ratio sensitivity to reinforcement occurrred on the two keys showed that this invariance of response despite changes in reinforcement interaction that were observed in absolute response rates on the constant VI 120-s schedule. Response rate on the constant VI 120-s schedule was inversely related to reinforcer rate on the varied key and the strength of this relation depended on the relative magnitude of reinforcers arranged on varied key. Independence of sensitivity to reinforcer-rate ratios from relative and absolute reinforcer magnitude is consistent with the relativity and independence assumtions of the matching law.     

Concurrent fixed-interval variable-ratio schedules and the matching relation

Five rats responded under concurrent fixed-interval variable-ratio schedules of food reinforcement. Fixed-interval values ranged from 50-seconds to 300-seconds and variable-ratio values ranged from 30 to 360; a five-second changeover delay was in effect throughout the experiment. The relations between reinforcement ratios obtained from the two schedules and the ratios of responses and time spent on the schedules were described by Baum's (1974) generalized matching equation. All subjects undermatched both response and time ratios to reinforcement ratios, and all subjects displayed systematic bias in favor of the variable-ratio schedules. Response ratios undermatched reinforcement ratios less than did time ratios, but response ratios produced greater bias than did time ratios for every subject and for the group as a whole. Local rates of responding were generally higher on the variable-ratio than on the fixed-interval schedules. When responding was maintained by both schedules, a period of no responding on either schedule immediately after fixed-interval reinforcement typically was followed by high-rate responding on the variable-ratio schedule. At short fixed-interval values, when a changeover to the fixed-interval schedule was made, responding usually continued until fixed-interval reinforcement was obtained; at longer values, a changeover back to the variable-ratio schedule usually occurred when fixed-interval reinforcement was not forthcoming within a few seconds, and responding then alternated between the two schedules every few seconds until fixed-interval reinforcement finally was obtained.     

Drug discrimination in rats under concurrent variable-interval variable-interval schedules

Eight rats were trained to discriminate pentobarbital from saline under a concurrent variable-interval (VI) VI schedule, on which responses on the pentobarbital-biased lever after pentobarbital were reinforced under VI 20 s and responses on the saline-biased lever were reinforced under VI 80 s. After saline, the reinforcement contingencies programmed on the two levers were reversed. The rats made 62.3% of their responses on the pentobarbital-biased lever after pentobarbital and 72.2% on the saline-biased lever after saline, both of which are lower than predicted by the matching law. When the schedule was changed to concurrent VI 50 s VI 50 s for test sessions with saline and the training dose of pentobarbital, responding on the pentobarbital-biased lever after the training dose of pentobarbital and on the saline-biased lever after saline became nearly equal, even during the first 2 min of the session, suggesting that the presence or absence of the training drug was exerting minimal control over responding and making the determination of dose-effect relations of drugs difficult to interpret. When the pentobarbital dose-response curve was determined under the concurrent VI 50-s VI 50-s schedule, responding was fairly evenly distributed on both levers for most rats. Therefore, 6 additional rats were trained to respond under a concurrent VI 60-s VI 240-s schedule. Under this schedule, the rats made 62.6% of their responses on the pentobarbital-biased lever after pentobarbital and 73.5% of their responses on the saline-biased lever after saline, which also is lower than the percentages predicted by perfect matching. When the schedule was changed to a concurrent VI 150-s VI 150-s schedule for 5-min test sessions with additional drugs, the presence or absence of pentobarbital continued to control responding in most rats, and it was possible to generate graded dose-response curves for pentobarbital and other drugs using the data from these 5-min sessions. The dose-response curves generated under these conditions were similar to the dose-response curves generated using other reinforcement schedules and other species.     

Variable-ratio versus variable-interval schedules: response rate, resistance to change, and preference

Two experiments asked whether resistance to change depended on variable-ratio as opposed to variable-interval contingencies of reinforcement and the different response rates they establish. In Experiment 1, pigeons were trained on multiple random-ratio random-interval schedules with equated reinforcer rates. Baseline response rates were disrupted by intercomponent food, extinction, and prefeeding. Resistance to change relative to baseline was greater in the interval component, and the difference was correlated with the extent to which baseline response rates were higher in the ratio component. In Experiment 2, pigeons were trained on multiple variable-ratio variable-interval schedules in one half of each session and on concurrent chains in the other half in which the terminal links corresponded to the multiple-schedule components. The schedules were varied over six conditions, including two with equated reinforcer rates. In concurrent chains, preference strongly overmatched the ratio of obtained reinforcer rates. In multiple schedules, relative resistance to response-independent food during intercomponent intervals, extinction, and intercomponent food plus extinction depended on the ratio of obtained reinforcer rates but was less sensitive than was preference. When reinforcer rates were similar, both preference and relative resistance were greater for the variable-interval schedule, and the differences were correlated with the extent to which baseline response rates were higher on the variable-ratio schedule, confirming the results of Experiment 1. These results demonstrate that resistance to change and preference depend in part on response rate as well as obtained reinforcer rate, and challenge the independence of resistance to change and preference with respect to response rate proposed by behavioral momentum theory.     

Within-subject testing of the signaled-reinforcement effect on operant responding as measured by response rate and resistance to change

Response rates under random-interval schedules are lower when a brief (500 ms) signal accompanies reinforcement than when there is no signal. The present study examined this signaled-reinforcement effect and its relation to resistance to change. In Experiment 1, rats responded on a multiple random-interval 60-s random-interval 60-s schedule, with signaled reinforcement in only one component. Response resistance to alternative reinforcement, prefeeding, and extinction was compared between these components. Lower response rates, and greater resistance to change, occurred in the component with the reinforcement signal. In Experiment 2, response rates and resistance to change were compared after training on a multiple random-interval 60-s random-interval 60-s schedule in which reinforcer delivery was unsignaled in one component and a response-produced uncorrelated stimulus was presented in the other component. Higher response rates and greater resistance to change occurred with the uncorrelated stimulus. These results highlight the significance of considering the effects of an uncorrelated signal when used as a control condition, and challenge accounts of resistance to change that depend solely on reinforcer rate.     

Does the context of reinforcement affect resistance to change?

Eight pigeons were trained on multiple schedules of reinforcement where pairs of components alternated in blocks on different keys to define 2 local contexts. On 1 key, components arranged 160 and 40 reinforcers/hr; on the other, components arranged 40 and 10 reinforcers/hr. Response rates in the 40/hr component were higher in the latter pair. Within pairs, resistance to prefeeding and resistance to extinction were generally greater in the richer component. The two 40/hr components did not differ in resistance to prefeeding, but the 40/hr component that alternated with 10/hr was more resistant to extinction. This discrepancy was interpreted by an algebraic model relating response strength to component reinforcer rate, including generalization decrement. According to this model, strength is independent of context, consistent with research on schedule preference.     

The role of discriminative stimuli in concurrent performances

Key pecking in pigeons was examined under concurrent and parallel arrangements of two independent and simultaneously available variable-interval schedules. Pecks on the changeover key alternated the schedule of reinforcement for responses on the main key. Under concurrent schedules, discriminative stimuli were paired with the reinforcement schedule arranged in each component and changeover responses also alternated these stimuli. Under parallel schedules, changeover responses alternated the effective reinforcement schedule, but did not change the discriminative stimulus. On concurrent procedures, changeover response rate was inversely related to the difference in reinforcement rate between the two components, whereas on parallel schedules no consistent relationship was found. With both schedules, absolute response and reinforcement rates were positively related, although for a given set of reinforcement frequencies, rates were often higher on the concurrent schedules. On concurrent schedules, relative response rates and relative times were equal to relative reinforcement rates. On parallel schedules these ratios were positively related, but response and time ratios were much smaller than were obtained with comparable concurrent schedules. This inequality was most pronounced when absolute reinforcement frequencies were lowest.     

Molar And Molecular Control In Variable-interval And Variable-ratio Schedules

Response rates are typically higher under variable-ratio than under variable-interval schedules of reinforcement, perhaps because of differences in the dependence of reinforcement rate on response rate or because of differences in the reinforcement of long interresponse times. A variable-interval-with-added-linear-feedback schedule is a variable-interval schedule that provides a response rate/reinforcement rate correlation by permitting the minimum interfood interval to decrease with rapid responding. Four rats were exposed to variable-ratio 15, 30, and 60 food reinforcement schedules, variable-interval 15-, 30-, and 60-s food reinforcement schedules, and two versions of variable-interval-with-added-linear-feedback 15-, 30-, and 60-s food reinforcement schedules. Response rates on the variable-interval-with-added-linear-feedback schedule were similar to those on the variable-interval schedule; all three schedules led to lower response rates than those on the variable-ratio schedules, especially when the schedule values were 30. Also, reinforced interresponse times on the variable-interval-with-added-linear-feedback schedule were similar to those on variable interval and much longer than those produced by variable ratio. The results were interpreted as supporting the hypothesis that response rates on variable-interval schedules in rats are lower than those on comparable variable-ratio schedules, primarily because the former schedules reinforce long interresponse times.     

Stimulus generalization of behavioral history: Interspecies generality and persistence of generalization gradients

Four pigeons were exposed to a tandem variable-interval (VI) fixed-ratio (FR) schedule in the presence of a 50-pixel (about 15 mm) square or an 80-pixel (about 24 mm) square and to a tandem VI differential-reinforcement-of-low-rate (DRL) schedule when a second 80-pixel or 50-pixel square was present. The values of the VI and FR schedules were adjusted to equate reinforcement rates in the two tandem schedules. Following this, a square-size continuum generalization test was administered under a fixed-interval (FI) schedule or extinction. In the first testing session, response frequency was a graded function of the similarity of the test stimuli to the training stimuli for all pigeons. These systematic generalization gradients persisted longer under the FI schedule than under extinction.     

Behavioral momentum in computer-presented discriminations in individuals with severe mental retardation

Behavioral momentum was examined in 2 individuals with severe mental retardation via within-subject manipulations of obtained reinforcer rates. Subjects performed self-paced discrimination problems presented on a touch screen computer monitor. Two different problems, Tasks A and B, alternated in blocks of 15 trials on a multiple schedule. Reinforcers were snack foods. The reinforcement schedule for Task A was continuous (fixed-ratio 1) and the schedule for Task B was continuous in some conditions and variable ratio in other conditions. Behavioral momentum was assessed in test sessions by prefeeding, presenting response-independent food, and making available alternatives to the tasks. When the obtained reinforcer rate for Task A was at least twice that for Task B, resistance to change was greater for Task A. When both reinforcer rates and response rates were a pproximately equal for the two tasks, resistance to change was approximately equal. These results are consistent with behavioral momentum effects. They extend previous findings with humans by examining momentum in self-initiated discrete-trial discrimination tasks with ratio schedules, and by isolating relative reinforcer rates as a controlling variable via within-subject manipulations.     

A pharmacological examination of the resistance-to-change hypothesis of response strength.

The effects of d-amphetamine sulfate, sodium pentobarbital, haloperidol, and cholecystokinin-octapeptide were examined within the context of Nevin's (1974, 1979) resistance-to-change hypothesis of response strength. In three experiments, rats' responding was reinforced by delivery of food under chained random-interval 30-s random-interval 30-s, multiple fixed-interval 30-s fixed-interval 120-s, or multiple random-interval 30-s random-interval 120-s schedules. Each rat received several doses of each drug and changes in response rate were measured. The resistance-to-change hypothesis predicts greater disruption of response rate relative to baseline in the initial component of the chained schedule and in the 120-s component of the multiple schedules. In the chained schedule cholecystokinin-octapeptide produced greater reductions in response rate relative to baseline in the initial component. However, no differences between components were observed with haloperidol or sodium pentobarbital, and high doses of d-amphetamine reduced response rate in the terminal component relatively more than in the initial component. In the multiple schedules either no differences were observed between components or response rate was reduced more relative to baseline in the 30-s component. The data fail to support the notion that drugs may be viewed within the same context as other response disruptors such as extinction, satiation, and the presentation of alternative reinforcement.     

Human performance on negative slope schedules of points exchangeable for money: a failure of molar maximization

Panel pressing was generated and maintained in 5 adult humans by schedules of points exchangeable for money. Following exposure to a variable-interval 30-s schedule and to a linear variable-interval 30-s schedule (which permitted points to accumulate in an unseen "store" in the absence of responding), subjects were exposed to a series of conditions with a point-subtraction contingency arranged conjointly with the linear variable-interval schedule. Specifically, points were added to the store according to the linear-variable interval 30-s schedule and were subtracted from the store according to a ratio schedule. Ratio value varied across conditions and was determined individually for each subject such that the subtraction contingency would result in an approximately 50% reduction in the rate of point delivery. Conditions that included the subtraction contingency were termed negative slope schedules because the feedback functions were negatively sloped across all response rates greater than the inverse of the variable-interval schedule, in this case, two per minute. Overall response rates varied inversely with the subtraction ratio, indicating sensitivity to the negative slope conditions, but were in excess of that required by accounts based on strict maximization of overall reinforcement rate. Performance was also not well described by a matching-based account. Detailed analyses of response patterning revealed a consistent two-state pattern in which bursts of high-rate responding alternated with periods of prolonged pausing, perhaps reflecting the joint influence of local and overall reinforcement rates.     

Resistance to reinforcement change in multiple and concurrent schedules assessed in transition and at steady state

Behavioral momentum theory relates resistance to change of responding in a multiple-schedule component to the total reinforcement obtained in that component, regardless of how the reinforcers are produced. Four pigeons responded in a series of multiple-schedule conditions in which a variable-interval 40-s schedule arranged reinforcers for pecking in one component and a variable-interval 360-s schedule arranged them in the other. In addition, responses on a second key were reinforced according to variable-interval schedules that were equal in the two components. In different parts of the experiment, responding was disrupted by changing the rate of reinforcement on the second key or by delivering response-independent food during a blackout separating the two components. Consistent with momentum theory, responding on the first key in Part 1 changed more in the component with the lower reinforcement total when it was disrupted by changes in the rate of reinforcement on the second key. However, responding on the second key changed more in the component with the higher reinforcement total. In Parts 2 and 3, responding was disrupted with free food presented during intercomponent blackouts, with extinction (Part 2) or variable-interval 80-s reinforcement (Part 3) arranged on the second key. Here, resistance to change was greater for the component with greater overall reinforcement. Failures of momentum theory to predict short-term differences in resistance to change occurred with disruptors that caused greater change between steady states for the richer component. Consistency of effects across disruptors may yet be found if short-term effects of disruptors are assessed relative to the extent of change observed after prolonged exposure.     

Accuracy of discrimination,rate of responding,and resistance to change

Pigeons were trained on multiple schedules in which responding on a center key produced matching-to-sample trials according to the same variable-interval 30-s schedules in both components. Matching trials consisted of a vertical or tilted line sample on the center key followed by vertical and tilted comparisons on the side keys. Correct responses to comparison stimuli were reinforced with probability .80 in the rich component and .20 in the lean component. Baseline response rates and matching accuracies generally were higher in the rich component, consistent with previous research. When performance was disrupted by prefeeding, response-independent food during intercomponent intervals, intrusion of a delay between sample and comparison stimuli, or extinction, both response rates and matching accuracies generally decreased. Proportions of baseline response rate were greater in the rich component for all disrupters except delay, which had relatively small and inconsistent effects on response rate. By contrast, delay had large and consistent effects on matching accuracy, and proportions of baseline matching accuracy were greater in the rich component for all four disrupters. The dissociation of response rate and accuracy with delay reflects the localized impact of delay on matching performance. The similarity of the data for response rate and accuracy with prefeeding, response-independent food, and extinction shows that matching performance, like response rate, is more resistant to change in a rich than in a lean component. This result extends resistance to change analyses from the frequency of response emission to the degree of stimulus control, and suggests that the strength of discriminating, like the strength of responding, is positively related to rate of reinforcement.     

Food-deprivation level alters the effects of morphine on pigeons'' key pecking.

Four pigeons pecked response keys under a multiple fixed-ratio 30 fixed-interval 5-min schedule of food presentation. Components alternated separated by 15-s timeouts; each was presented six times. Pigeons were maintained at 70%, 85%, and greater than 90% of their free-feeding weights across experimental conditions. When response rates were stable, the effects of morphine (0.56 to 10.0 mg/kg) and saline were investigated. Morphine reduced response rates in a dose-dependent manner under the fixed-ratio schedule and at high doses under the fixed-interval schedule. In some cases, low doses of morphine increased rates under the fixed-interval schedule. When pigeons were less food deprived, reductions in pecking rates occurred at lower doses under both schedules for 3 of 4 birds compared to when they were more food deprived. When pigeons were more food deprived, low doses of morphine increased rates of pecking in the initial portions of fixed intervals by a greater magnitude. Thus, food-deprivation levels altered both the rate-decreasing and rate-increasing effects of morphine. These effects may share a common mechanism with increased locomotor activity produced by drugs and with increased drug self-administration under conditions of more severe food deprivation.     

Arousal, changeover responses, and preference in concurrent schedules

Pigeons were trained on multiple schedules that provided concurrent reinforcement in each of two components. In Experiment 1, one component consisted of a variable-interval (VI) 40-s schedule presented with a VI 20-s schedule, and the other a VI 40-s schedule presented with a VI 80-s schedule. After extended training, probe tests measured preference between the stimuli associated with the two 40-s schedules. Probe tests replicated the results of Belke (1992) that showed preference for the 40-s schedule that had been paired with the 80-s schedule. In a second condition, the overall reinforcer rate provided by the two components was equated by adding a signaled VI schedule to the component with the lower reinforcer rate. Probe results were unchanged. In Experiment 2, pigeons were trained on alternating concurrent VI 30-s VI 60-s schedules. One schedule provided 2-s access to food and the other provided 6-s access. The larger reinforcer magnitude produced higher response rates and was preferred on probe trials. Rate of changeover responding, however, did not differ as a function of reinforcer magnitude. The present results demonstrate that preference on probe trials is not a simple reflection of the pattern of changeover behavior established during training.     

The generality of selective observing

Four rats obtained food pellets by poking a key and 5-s presentations of the discriminative stimuli by pressing a lever. Every 1 or 2 min, the prevailing schedule of reinforcement for key poking alternated between rich (either variable-interval [VI] 30 s or VI 60 s) and lean (either VI 240 s, VI 480 s, or extinction) components. While the key was dark (mixed-schedule stimulus), no exteroceptive stimulus indicated the prevailing schedule. A lever press (i.e., an observing response), however, illuminated the key for 5 s with either a steady light (S+), signaling the rich reinforcement schedule, or a blinking light (S-), signaling the lean reinforcement schedule. One goal was to determine whether rats would engage in selective observing (i.e., a pattern of responding that maintains contact with S+ and decreases contact with S-). Such a pattern was found, in that a 5-s presentation of S+ was followed relatively quickly by another observing response (which likely produced another 5-s period of S+), whereas exposure to S- resulted in extended breaks from observing. Additional conditions demonstrated that the rate of observing remained high when lever presses were effective only when the rich reinforcement schedule was in effect (S+ only condition), but decreased to a low level when lever presses were effective only during the lean reinforcement component (S- only condition) or when lever presses had no effect (in removing the mixed stimulus or presenting the multiple-schedule stimuli). These findings are consistent with relativistic conceptualizations of conditioned reinforcement and extend the generality of selective observing to procedures in which the experimenter controls the duration of stimulus presentations, the schedule components both offer intermittent food reinforcement, and rats serve as subjects.